As stated in the original grant, "a major goal of research in Clinical Pharmacology is to characterize and understand the Therapeutic Response Surface, the quantitative relationships between patient factors, drug dosage, drug exposure, and drug effects .... " Data analyses according to predictive (mechanistic) hierarchical dynamic pharmacokinetic-pharmacodynamic (PKPD) models (so-called "population" PKPD models), "are increasingly seen as a means to gain knowledge about the response surface." GM26676 was funded to develop and implement methods for such analyses, and progress reports since our last renewal document our considerable success in doing so. Indeed, that success justifies this supplementary application: we have been encouraged increasingly to apply the mechanistic modeling to every larger and more complex problems, and now confront serious limitations imposed by the computational burden associated with optimizing large-scale dynamic models to large-scale data sets, a limitation not foreseen in the original application. We propose to implement and test a new methodology for model optimization founded on approximating the solution to the PKPD system dynamics conditional on the population parameters, which is the main computational cost of evaluating and maximizing the likelihood function through which the model is produced. The approximation is accomplished by mixing the techniques of solution mapping and computer experiments, as successfully applied to similar problems in engineering. The computational burden of optimizing the likelihood function is thereby reduced by over an order of magnitude. The specific aims of this supplementary application continue the three of the original application, and are: Aim 4: To develop, apply, and evaluate solution-mapping methods to the solution to large systems of linked differential equations, by 4.A. Defining (1) subject-level PKPD differential equation models, and (2) population level hierarchical models of increasing complexity to be used in testing solution-mapping approximations; 4.B. Developing/applying algorithms and prototype software for solution-mapping approximations to models (A.1) incorporating designs for efficient computer experiments to define solution-mapping approximations. 4.C. Assessing performance of methods (4.B) on models (4.A.1) in terms of ability to precisely estimate models (4.A.2); and Aim 5: Implementing successful methods of Aim (4) in prototype exportable software that naturally interfaces with NONMEM.